1. Field of the Invention
The invention disclosed herein relates to analysis of resistivity data collected in geophysical exploration and, in particular, to techniques for improved speed and precision of numerical simulations.
2. Description of the Related Art
Exploration for oil, gas and other hydrocarbons uses a variety of technologies embodied in various tooling and instrumentation. One important technology makes use of resistivity measurements. In resistivity measurements, an electric current is directed into formations surrounding a wellbore and various measurements are performed. Data collected from measurements is then interpreted in a variety of ways. Techniques include use of data inversion and simulation.
Data inversion is used to determine a property of an earth formation from the data collected by the resistivity measurements. To generate a data inversion algorithm, a simulation of a resistivity tool is used to estimate the data that would be obtained from the tool using known properties of the formation. Both data inversion and simulation require an accurate and precise method of simulating measurements performed by the resistivity tool.
It is known that in existing methods, (such as for two-dimensional electromagnetic simulation, as may be used in studies and data inversion), simulation precision deteriorates when a grid cell is one of heterogeneous or filled with a highly conductive material (such as metal), so that its size is much greater than the skin depth.
Thus, what are needed are techniques for overcoming drawbacks of the classical “parallel-serial” way of material averaging (inside a heterogeneous discretization cell), both by theoretical analysis and numerical experiments. Preferably, the technique provides precise numerical results over existing solutions. Among other things, the techniques should enable accurate simulation of problems with thin skin layers on coarse grids.